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Geometry, Physics, and Symmetries

Group “Fundamental Interactions”

Our activities are centered on the mathematical description of physical laws, in particular laws that govern fundamental interactions. The necessary tools are often of geometric, algebraic, combinatorial, analytic or functional nature. Some results or problems lead to the emergence of new mathematical structures needing a dedicated study. Others have direct physical applications.

Fundamental laws of nature, at the classical level, are naturally expressed in terms of geometry (for instance the notion of connection on a bundle appears in our understanding of both gravity and strong or electroweak interactions), and symmetries of the physical world are usually described, classically, by group theoretical constructions, in particular representation theory. Geometry finds its roots in the study of symmetries but one knows that mechanics itself uses geometry, in particular symplectic geometry, for its own formulation. A quantum description of physics requires not only the above tools but also appropriate generalizations of these notions. Approaches leading to theories of quantum gravity using non-commutative geometry, for instance, need mathematical descriptions where space-time (actually its algebra of functions) is replaced by a non-commutative algebra; moreover many developments of quantum field theory use generalizations of the notion of group, for instance supersymmetric theories use Lie super-algebras, and conformal field theory or string theory, as well as the theory of integrable systems, use concepts coming from affine Lie algebras and quantum groups.
Our activities focus around the above themes.

Directory of Members

Attard Jérémy PhD candidate
Email
Bizi Nadir PhD candidate
Email
BULGAKOVA Daria PhD candidate
Email
Coquereaux Robert Researcher
+33.4.91.26.95.18 Email
Duval Christian Emeritus
+33.4.91.26.97.97 Email
Giovannetti Gabriel ATER
Email
Iochum Bruno Emeritus
+33.4.91.26.97.96 Email
Krajewski Thomas University faculty
+33.4.91.26.95.61 Email
Lazzarini Serge University faculty
Chef de l’équipe « Géométrie, Physique et Symétries »
Web editor
Correspondant FRUMAM
+33.4.91.26.97.94 Email
Luminet Jean-Pierre Guest
+33.4.91.26.95.19 Email
Marsot Loïc PhD candidate
Email
Masson Thierry Researcher
Communications manager
Correspondant valorisation
+33.4.91.26.97.94 Email
Ogievetsky Oleg University faculty
+33.4.91.26.95.33 Email
Schücker Thomas University faculty
Chef du Groupe « Interactions fondamentales »
+33.4.91.26.95.61 Email
Triay Roland University faculty
+33.4.91.26.95.19 Email

List of Publications

109 results
Thesis
Cédric Fournel
Théories de jauge et connexions généralisées sur les algébroïdes de Lie transitifs
Mathematical Physics [math-ph]. Aix-Marseille Université, 2013. English
Conference paper
Galliano Valent, Christian Duval, Vsevolod Shevchishin
Explicit metrics for a class of two-dimensional cubically superintegrable systems
Finite dimensional integrable systems: on the crossroad of algebra, geometry and physics, Jul 2013, Marseille, France. Journal of Geometry and Physics, 87, pp.354-372, 2015, 〈http://www.cpt.univ-mrs.fr/fdis13/〉. 〈10.1016/j.geomphys.2014.08.004〉
Journal article
Robert Coquereaux, Jean-Bernard Zuber
Drinfeld doubles for finite subgroups of SU(2) and SU(3) Lie groups
Symmetry, Integrability and Geometry : Methods and Applications, Integrability and Geometry : Methods and Applications, 2013, 9 (039), http://www.emis.de/journals/SIGMA/2013/039/. 〈10.3842/SIGMA.2013.039〉
Journal article
Cédric Fournel, Serge Lazzarini, Thierry Masson
Formulation of gauge theories on transitive Lie algebroids
Journal of Geometry and Physics, Elsevier, 2013, 64, pp.174. 〈10.1016/j.geomphys.2012.11.005〉
Journal article
Galliano Valent
On a class of integrable systems with a quartic first integral
Regular and Chaotic Dynamics, MAIK Nauka/Interperiodica, 2013, 18 (04), pp.394-424. 〈10.1134/S1560354713040060〉
Journal article
Christian Duval, P. A. Horvathy, P. M. Zhang
Transverse Shifts in Paraxial Spinoptics
Journal of Optics, Institute of Physics (IOP), 2013, 15 (014005), 4pp. 〈10.1088/2040-8978/15/1/014005〉
Journal article
Gérard H. E. Duchamp, Nguyen Hoang-Nghia, Thomas Krajewski, Adrian Tanasa
Recipe theorem for the Tutte polynomial for matroids, renormalization group-like approach
Advances in Applied Mathematics, Elsevier, 2013, 51 (03), pp.345-358. 〈10.1016/j.aam.2013.04.006〉
Journal article
Christian Duval, Mark Gotay
Quantization via Deformation of Prequantization
Reports on Mathematical Physics, Elsevier, 2012, 70 (03), pp.361-374. 〈10.1016/S0034-4877(12)60051-2〉
Journal article
Thomas Schucker, Sami R. Zouzou
On a weak Gauss law in general relativity and torsion
Classical and Quantum Gravity, IOP Publishing, 2012, 29 (24), pp.245009. 〈10.1088/0264-9381/29/24/245009〉
Journal article
Thomas Schucker
Higgs-mass predictions
Acta Physica Polonica B, Jagellonian University, Cracow, 2012, 43 (9), pp.1863. 〈10.5506/APhysPolB.43.1863〉
109 results

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